Information on Result #703110
Linear OA(333, 259, F3, 9) (dual of [259, 226, 10]-code), using construction XX applied to C1 = C([239,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([239,6]) based on
- linear OA(326, 242, F3, 8) (dual of [242, 216, 9]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,4}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(321, 242, F3, 7) (dual of [242, 221, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(331, 242, F3, 10) (dual of [242, 211, 11]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,6}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(316, 242, F3, 5) (dual of [242, 226, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 6, F3, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(333, 251, F3, 2, 9) (dual of [(251, 2), 469, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(333, 251, F3, 3, 9) (dual of [(251, 3), 720, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(333, 251, F3, 4, 9) (dual of [(251, 4), 971, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(333, 251, F3, 5, 9) (dual of [(251, 5), 1222, 10]-NRT-code) | [i] | ||
| 5 | Digital (24, 33, 251)-net over F3 | [i] | ||
| 6 | Linear OA(334, 261, F3, 9) (dual of [261, 227, 10]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(333, 129, F3, 2, 9) (dual of [(129, 2), 225, 10]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(333, 86, F3, 3, 9) (dual of [(86, 3), 225, 10]-NRT-code) | [i] | ||